Extracting metric metric from RHVAE

[axu-git]

I am using RHVAE.

i) Is the learned metric $G$ (or $G^{-1}$) an array (i.e., multidimensional matrix)? I'm confused because the formula for $G^{-1}$ (i.e., equation 8 in "Data Augmentation in High ...") involves terms $L_{\psi_i}$. $L_{\psi_i}$ are parameterized by neural networks which makes me think they are not matrices/multidimensional arrays but rather neural networks.

Supposing the answer to (i) is yes (i.e., $G$ (or $G^{-1}$) is a multidimensional array):
ii) If $G$ (or $G^{-1}$) is an array, let's say the latent_dim = n. What is the dimension of the learned metric $G$ (or $G^{-1}$)?

iii) In "Geometry-Aware Hamiltonian VAE" section 4.3.1, you describe computing $A(z)$ based on eigenvalues. Does this only work in the case where latent_dim = 2? I am assuming here that the answer to (ii) is that for latent_dim > 2, the rank of the tensor is also > 2, which means you cannot define an eigenvalue (which are defined only for 2d matrices).

Regardless of the answer to (i):
iv) Suppose I train a RHVAE model using pythae. How can I extract the learned metric? Is there some code that lets me easily do this?

Thanks!